A general affine connection decomposes into metric, symmetric, mixed, and vector parts; in symmetric spacetimes the transverse-traceless part carries no local degrees of freedom and reduces to a residual gauge.
A comparative review of recent researches in geometry
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abstract
Felix Klein's so-called Erlangen Program was published in 1872 as professoral dissertation. It proposed a new solution to the problem how to classify and characterize geometries on the basis of projective geometry and group theory. The given translation was made in 1892 by Dr. M. W. Haskell and transcribed by N. C. Rughoonauth. We replaced bibliographical data in text and footnotes with pointers to a complete bibliography section.
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Decomposition of the connection in affine models of gravity: Can the connection tell us something about the metric?
A general affine connection decomposes into metric, symmetric, mixed, and vector parts; in symmetric spacetimes the transverse-traceless part carries no local degrees of freedom and reduces to a residual gauge.